Curiosity as Epistemic Displacement Drive: Information Gap as D(ξ), Exploration as Return Path, and Wonder as Ground State Expansion

We apply the Displacement Framework to curiosity and exploration, formalizing curiosity as D(xi_epistemic) — the gap between what is known and what feels needed to know. Loewenstein's Information Gap Theory is formalized as displacement: when a gap is perceived, D(xi_info) > 0, and curiosity is the gradient pointing toward epistemic return. Twelve formal propositions are derived: curiosity as epistemic displacement, exploration as epistemic return path, curiosity intensity and gap salience, diversive vs. specific curiosity as different return paths (Litman — diversive curiosity reduces D by expanding S0; specific curiosity reduces D by acquiring targeted knowledge), the curiosity-anxiety boundary (same D(xi_info), different landscape configuration via assessed closability — the gap feels like curiosity when closable, anxiety when not), exploration-exploitation as return path optimization, dopamine as epistemic gradient signal, the curiosity wrong attractor (perpetual novelty-seeking and internet rabbit holes where S0_info is perpetually redefined preventing genuine return), curiosity-based learning as active gradient tracking, wonder as simultaneous epistemic displacement plus S0 expansion (the connection between curiosity and awe), curiosity suppression as gradient flattening (four mechanisms: authoritarian contexts, trauma, learned helplessness, rote education), and scientific method as formal curiosity return path (hypothesis as named D, experiment as planned return path execution). 32 citations including Loewenstein, Berlyne, Litman, Kashdan, Kidd/Hayden, Deci/Ryan, Gruber, Kang, Schultz, and Kuhn.